# A function that is naturally periodic?

• Feb 24th 2009, 12:42 PM
ruthvik
A function that is naturally periodic?
ok guys, im having trouble with this problem
this is due very soon

this was the question given

Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

Identify the period.

Graph the function.

what does it mean by naturally periodic? maybe i can do it if i know what it means, also how do i figure out a period of a regular function? i only know how to do it to trig functions

any help is appreciated, thanks
• Feb 24th 2009, 01:01 PM
Plato
Quote:

Originally Posted by ruthvik
Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

Use the floor function: $\displaystyle f(x) = x - \left\lfloor x \right\rfloor$
• Feb 24th 2009, 01:05 PM
sinewave85
Quote:

Originally Posted by ruthvik
ok guys, im having trouble with this problem
this is due very soon

this was the question given

Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

Identify the period.

Graph the function.

what does it mean by naturally periodic? maybe i can do it if i know what it means, also how do i figure out a period of a regular function? i only know how to do it to trig functions

any help is appreciated, thanks

A function that is naturally periodic is any function based on a cyclical variable. One good "natural" cyclical variable is clock time. You can set up a simple equation with time as the variable, like y = 2t, and they graph the equation with t as the horizontal axis.
• Feb 24th 2009, 01:08 PM
ruthvik
Quote:

Originally Posted by sinewave85
A function that is naturally periodic is any function based on a cyclical variable. One good "natural" cyclical variable is clock time. You can set up a simple equation with time as the variable, like y = 2t, and they graph the equation with t as the horizontal axis.

i dont understand what cyclical variables are

also, i dont know what that equation the other guy made, i can graph it but im thinking of this answer in more simple terms
• Feb 24th 2009, 01:27 PM
sinewave85
Quote:

Originally Posted by ruthvik
i dont understand what cyclical variables are

also, i dont know what that equation the other guy made, i can graph it but im thinking of this answer in more simple terms

Sorry, the answer I gave won't work because it it not a function -- it wont pass the vertical line test. I am trying to think of a way to construct a simple periodic function -- one the oscillates up and down -- without using a sin function.
• Feb 24th 2009, 01:49 PM
Plato
What do you not like about my function? It has a natural period of 1.
• Feb 24th 2009, 01:52 PM
ruthvik
Quote:

Originally Posted by Plato
What do you not like about my function? It has a natural period of 1.

i never learned that function, so i cannot use it, otherwise i would have : D

thanks though
• Feb 24th 2009, 01:57 PM
Plato
Quote:

Originally Posted by ruthvik
i never learned that function, so i cannot use it, otherwise i would have.

You mean that you never learned the greatest integer function?
The floor function is just a more modern notation for that.
• Feb 24th 2009, 02:14 PM
ruthvik
Quote:

Originally Posted by Plato
You mean that you never learned the greatest integer function?
The floor function is just a more modern notation for that.

oh wow?? really? i learned GINT, but tell me plato, if my teacher asks how i got this, how will i explain to him? how can i graph this on paper? because i only learned what it is , will it work if i use plug in for x and stuff?
• Feb 24th 2009, 02:28 PM
Plato
For every x, $\displaystyle \left\lfloor x \right\rfloor \leqslant x < \left\lfloor x \right\rfloor + 1\; \Rightarrow \;0 \leqslant x - \left\lfloor x \right\rfloor < 1$.

As you can see the graph goes from 0 to 1 (never equal to 1) between any two consecutive integers.
• Feb 24th 2009, 03:39 PM
ruthvik
Quote:

Originally Posted by Plato
For every x, $\displaystyle \left\lfloor x \right\rfloor \leqslant x < \left\lfloor x \right\rfloor + 1\; \Rightarrow \;0 \leqslant x - \left\lfloor x \right\rfloor < 1$.

As you can see the graph goes from 0 to 1 (never equal to 1) between any two consecutive integers.

this might be a stupid question but when i graph it, there is a open circle on the top part right? like (1,1)

thanks btw, your eq was a good example
• Feb 24th 2009, 03:51 PM
Plato
Quote:

Originally Posted by ruthvik
this might be a stupid question but when i graph it, there is a open circle on the top part right? like (1,1)

thanks btw, your eq was a good example

yes